ITM Web Conf.
Volume 12, 2017The 4th Annual International Conference on Information Technology and Applications (ITA 2017)
|Number of page(s)||5|
|Section||Session 3: Computer|
|Published online||05 September 2017|
Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale
Department of Statistics North China University of Technology, Beijing, 100144, China
In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued square integrable martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and set-valued square integrable martingale integral equation. The existence and uniqueness of solution to set-valued stochastic integral equation are proved. The discussion will be useful in optimal control and mathematical finance in psychological factors.
© The Authors, published by EDP Sciences, 2017
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